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A careful analysis of the maximally extended metrics of Schwarzschildmanifold shows that the original Schwarzschild's solution (1916) andBrillouin's solution (1923) are the only ones that are adequate from thephysical standpoint. Contrary to the other maximally extended metrics, theyrepresent faithfully the gravity field created by the mass-point.

Schwarzschild manifold and non-regular coordinate transformations (A critico-historical Note)